Halicharan Narzary put Hyderabad ahead at the break but saw his header cancelled out by Cole Alexander in the second half.
Majumder made a slew of saves to keep CFC at bay for more than an hour after the red-and-gold were reduced to 10 players following Ajay Chhetri's send-off in the first-half.
NorthEast United FC defeated Jamshedpur FC 2-1 to end their seven-game winless streak in the early kick-off.
The calmness and reassurance Blasters exhibited against an East Bengal side which remained undefeated in their last five games was commendable.
Table-toppers Mumbai stretched their unbeaten run to 10 games.
Neville headed home in the injury time to salvage a point for the Kolkata giants.
A brace from Jorge Ortiz and Naveen Kumar’s brilliance in the goal helped FC Goa script a 3-0 win.
Robbie Fowler's East Bengal are unbeaten in their last five games, securing two wins on the way.
Goncalves scored in the 15th and 21st minutes for Chennayin before Diego Mauricio struck a screamer in the 64h minute to give Odisha some hope.
Luis Machado (27') opened the scoring for the Highlanders but Rahul Bheke (49') cancelled out his goal after the break to help the Blues salvage a point.